Problem: If $x \bigtriangledown y = xy+3x-y$ and $x \bigtriangleup y = 7x-3y$, find $-5 \bigtriangledown (-2 \bigtriangleup -4)$.
Answer: First, find $-2 \bigtriangleup -4$ $ -2 \bigtriangleup -4 = (7)(-2)-(3)(-4)$ $ \hphantom{-2 \bigtriangleup -4} = -2$ Now, find $-5 \bigtriangledown -2$ $ -5 \bigtriangledown -2 = (-5)(-2)+(3)(-5)-(-2)$ $ \hphantom{-5 \bigtriangledown -2} = -3$.